We prove also that the operations we propose are consistent with the ones of. Hesitant fuzzy rough sets deal with the lower and upper approximations in a hesitant fuzzy domain. Abstractintuitionistic fuzzy sets ifs are a generalization of fuzzy sets where the membership is an interval. Distance and similarity measures for hesitant fuzzy sets. A study on intervalvalued antihesitant fuzzy subnearrings. This paper focuses to extend this approach on a lattice and shows that two large application concepts of the fuzzy set theory namely resolution identity and representation theorem are true under this extended definition. A hesitant fuzzy hf set a on the crisp set u consists of ha, a mapping that assigns a subset hax of 0,1 with every. Rough approximations on hesitant fuzzy sets igi global. Pdf hesitant fuzzy set and its extensions researchgate. To accommodate more complex environment, several extensions of hfs have been presented, such as intervalvalued hesitant fuzzy set 5, 44, hesitant triangular fuzzy set 47, 51, hesitant. Hesitant fuzzy relation that is reflexive symmetric and transitive hesitant fuzzy set. Hwang and yoon 1981 first developed topsis to madm problems. Pdf knowledge measure of hesitant fuzzy set and its. Given a fixed set u, a dual hesitant fuzzy set dhfs is represented as in eq.
Pdf to address the complex multiple criteria decisionmaking mcdm problems in practice, this article proposes the picture hesitant fuzzy set phfs. Request pdf hesitant fuzzy sets several extensions and generalizations of fuzzy sets have been introduced in the literature, for example, atanassovs intuitionistic fuzzy sets. Firstly, a new entropy measure of hesitant fuzzy sets is constructed, then the weights are obtained using the entropy weight method, and positive. Its basic algebraic properties are set forth, and the model is linked to other successful models in the literature. Research article correlation measures of dual hesitant fuzzy sets.
Hesitant fuzzy topsis based investment projects selection problem. Intuitionistic fuzzy set ifs theory was first proposed by. Jan 01, 20 thus several generalizations and extensions of zfss are developed, such as type2 fuzzy sets, typen fuzzy sets, intuitionistic fuzzy sets ifss, fuzzy multisets and hesitant fuzzy sets. In reality, the membership degrees of a certain element x to m are not necessarily real numbers. A series of score functions for hesitant fuzzy sets. Intervalvalued hesitant fuzzy sets ivhfss, as an extension of hesitant fuzzy sets, can account for the membership degrees of an element to a given set. A hesitant fuzzy soft set is a mapping from parameters to hu. A decision support model for hotel recommendation based on. Pdf hesitant fuzzy linguistic terms sets for decision. Construct the decision matrix 4 and torra 2010 first proposed the concept of hesitant fuzzy set hfs. This paper extends pythagorean hesitant fuzzy environments to intervalvalued pythagorean hesitant fuzzy environments and proposes the concept of intervalvalued pythagorean hesitant fuzzy set ivphfs, which allows the membership of each object to be. Nov 28, 2020 request pdf on hesitant fuzzy sets and decision intuitionistic fuzzy sets ifs are a generalization of fuzzy sets where the membership is an interval. Pdf this book provides the readers with a thorough and systematic introduction to hesitant fuzzy theory. In this connection, many wellknown magdm methods have been extended to.
This paper extends pythagorean hesitant fuzzy environments to intervalvalued pythagorean hesitant fuzzy environments and proposes the concept of intervalvalued pythagorean hesitant fuzzy set ivphfs, which allows the membership of each object. To date, studies on hfss have mainly focused on three aspects, namely, hesitant fuzzy aggregation operators, multicriteria decision making mcdm methods, and hesitant fuzzy information measures. The notion of hesitant fuzzy sets together with hesitant fuzzy negations. Letmi be the set of all fuzzy sets of type ion 0,1. Xu and xia 17 proposed a variety of distance measures for hesitant fuzzy sets. It is a parameterised family of hesitant fuzzy subsets of. Hesitant fuzzy multiattribute decision making method based on a. Yu 43 gave the concept of triangular hesitant fuzzy sets and used it for the solution of decisionmaking problems. Hesitant fuzzy sets torra 2010 international journal of. Request pdf on hesitant fuzzy sets and decision intuitionistic fuzzy sets ifs are a generalization of fuzzy sets where the membership is an interval. Aug 01, 2015 however, type2 fuzzy sets are difficult to work with, so in 2009 hesitant sets were introduced by torra see, as an intermediate kind of fuzzy sets.
Because of the discrepancy of set itself, the elements of hesitant fuzzy sets cant be repeated, type2 hesitant fuzzy sets solve the mainly defect. The definition of the complement of a hesitant fuzzy set is straightforward. In recent decades, several types of sets, such as fuzzy sets, intervalvalued fuzzy sets, intuitionistic fuzzy sets, intervalvalued intuitionistic fuzzy sets, type 2 fuzzy sets, type fuzzy sets, and hesitant fuzzy sets, have been introduced and investigated widely. The related notion of expanded hesitant fuzzy set 29 xhfs can be used for similar purposes.
International journal of intelligent systems, 2014. A novel magdm approach with proportional hesitant fuzzy. Group decisionmaking for hesitant fuzzy sets based on. To date, studies on hfss have mainly focused on three aspects, namely, hesitant fuzzy aggregation operators, multicriteria decision making mcdm methods, and hesitant fuzzy. Buy this book isbn 9783319047119 digitally watermarked, drmfree included format. A hesitant fuzzy set, allowing the membership of an element to be a set of several possible values, is very useful to express peoples hesitancy in daily life. New operations over interval valued intuitionistic. Introduction of hesitant fuzzy rough sets would facilitate the use of rough set based techniques to hesitant fuzzy environment.
The membership function of a hesitant set assigns a subset of the closed interval 0, 1 instead of a fuzzy set to each point. A novel magdm approach with proportional hesitant fuzzy sets. Intervalvalued hesitant fuzzy sets have been used in the applications of group decisionmaking in 28,3740. Decision making with uncertainty using hesitant fuzzy sets. Identify the set of available alternatives and criteria. Hesitant fuzzy subset of the cartesian product of several crisp sets equivalence hesitant fuzzy relation. The hesitant fuzzy sets are a new efficient mathematical approach to study imprecise, uncertain, or incomplete knowledge.
Introduction to hesitant fuzzy set and its application in. Uncertainty measures for probabilistic hesitant fuzzy sets in multiple. Hesitant fuzzy soft topology and its applications to multi. Basic operationsgiven an hesitant fuzzy set h, we define below its lower and upper bound, it is clear that given an hesitant fuzzy set h, the pair of functions h. We introduce the notions of hesitant fuzzy semiprime sets. Fuzzy reliability based on hesitant and dual hesitant fuzzy. Next, the interval numbers were introduced to extend the membership function of hfs and the intervalvalued hesitant fuzzy set ivhfs theory. This special issue consists of five papers devoted to different. Typical hesitant fuzzy sets evaluating strategies in gdm. A decision support model for hotel recommendation based. This paper contributes a novel and advanced distance measure between intuitionistic hesitant fuzzy sets ihfss. Typical hesitant fuzzy sets evaluating strategies in gdm applying consensus measures monica matzenauer aand renata reiser and helida santosb and benjamin bedregalc appgc, cdtec, ufpel, pelotas rs, brazil, fmonica. Information systems on hesitant fuzzy sets igi global.
In this paper, we propose dual hesitant fuzzy sets dhfss, which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant. Qrung probabilistic dual hesitant fuzzy sets and their. In current scenario, the extension of fuzzy sets theory 28 so called hesitant fuzzy set which was introduced by torra 22 deals with the general. Pdf hesitant fuzzy sets theory studies in fuzziness and. An extension of a classical notion of a set whose elements have degrees of membership hesitant fuzzy relation.
Pentagonal hesitant fuzzy multiattribute international. We attempt to illustrate the advantages of applying hesitant fuzzy set to specialists and physicians. Hesitant fuzzy sets hfss were first introduced by torra 4 and torra and narukawa 5, it permits the membership degree of an element to a set to be represented as several possible values between 0 and 1. X evaluates the optional six houses under various attributes with hesitant fuzzy element. Research article correlation measures of dual hesitant. New operations over interval valued intuitionistic hesitant fuzzy set said broumi florentin smarandache abstract hesitancy is the most common problem in decision makingfor which hesitant fuzzy set, can be considered as a useful tool allowing several possible degrees of membership of. Picture hesitant fuzzy set and its application to multiple. In section 3, four new operations on interval valued intuitionistic hesitant fuzzy sets have been proposed and some properties of these operations are proved. In spite of the quick and important growth of interesting and novel research contributions on hesitant fuzzy sets, their different extensions and applications, a large number of improvements are still to be done and problems to be solved by using hesitant fuzzy tools and models. Logicfuzzy set theory and its applicationsintuitionistic fuzzy setsan. Spherical hesitant fuzzy sets shfss is the triplet having positive, neutral, and negative membership grades in the form of sets consider some values in 0,1. Mcgdm with hesitant twotuple linguistic information and by using trapezoidal valued hfss is discussed in 41,42. We introduce the notions of hesitant fuzzy semiprime sets and. Hesitant fuzzy multiattribute decision making based on.
New operations over interval valued intuitionistic hesitant. The main goal of this publication is to show that the basic constructions in the theories of fuzzy sets, fuzzy soft sets, fuzzy hesitant sets or intuitionistic fuzzy sets have a common background, based on the theory of monads in categories. Applications of hesitant fuzzy sets to completely regular. In section 2 the notion of fuzzy sets together with fuzzy negations and other properties are provided. Intervalvalued pythagorean hesitant fuzzy set and its. Pdf ebooks can be used on all reading devices immediate ebook.
We introduce a new view for applying hesitant fuzzy set in mcdm and data mining problems. Hesitant fuzzy soft set and its applications in multicriteria decision. Fuzzy sets, hesitant fuzzy sets, proportional hesitant fuzzy sets, multiattribute group decision making. We prove that the envelope of the hesitant fuzzy sets is an intuitionistic fuzzy set. Mar 01, 2011 hesitant fuzzy set permits the membership having a set of one about the first four types of fuzzy sets, however, little has been done about sed the relationship between hesitant fuzzy set and other three kinds of fuzzyhesitant fuzzy information aggregation in decision making q meimei xia, zeshui xu. Intuitionistic fuzzy sets atanassov 1986, type 2 fuzzy sets mizumoto and tanaka 1976 and fuzzy multisets miyamoto 2000 are just some of the most accepted ones. Fuzzy reliability based on hesitant and dual hesitant. Properties of intervalvalued hesitant fuzzy sets ios press. In spite of the quick and important growth of interesting and novel research contributions on hesitant fuzzy sets, their different extensions and applications, a large number of. The purpose of this paper is to extend the soft groups to the hesitant fuzzy set, and, thus, we establish a new soft group model named hesitant fuzzy soft group. Mar 12, 2010 several extensions and generalizations of fuzzy sets have been introduced in the literature, for example, atanassovs intuitionistic fuzzy sets, type 2 fuzzy sets, and fuzzy multisets. Dual hesitant fuzzy group decision making method and its. In this case, we try to model hesitancy and uncertainty existing in the nature of some medical application to hesitant fuzzy sets. Jun 01, 2011 multicriteria linguistic decision making based on hesitant fuzzy linguistic term sets and the aggregation of fuzzy sets information sciences, volume 286, 2014, pp.
A note on operations of hesitant fuzzy sets atlantis press. Molodtsovs soft set theory is a newly emerging mathematical tool to handle uncertainty. May 02, 2020 the purpose of this research study is to extend the multiattribute group decisionmaking magdm methods to hesitant fuzzy soft set hfs set, hesitant fuzzy soft topology hfstopology and hfshausdorff spaces in group decisionmaking environment, as hfs set is more superior tool to capture vagueness, hesitancy and incompleteness in individual evaluations. Hesitant fuzzy topsis based investment projects selection. Hesitant fuzzy sets torra 2010 international journal. Xu and xia 2011 developed the distance and similarity measures for hfss and proposed an. Dual hesitant fuzzy set can re ect human s hesitance more objectively than the other classical extensions of fuzzy set intuitionistic fuzzy set, type fuzzy set tfs, hesitant fuzzy set, etc. For convenience, we call a hesitant fuzzy element hfe and the set of all hfes. As a generalization of a fuzzy set, torra and narukawa in 9 and torra in 10 proposed notion of a hesitant fuzzy set hfs and its application in decisionmaking. Several extensions and generalizations of fuzzy sets have been introduced in the literature, for example, atanassovs intuitionistic fuzzy sets, type 2 fuzzy sets, and fuzzy multisets. Semilattices of hesitant fuzzy sets with union and intersection are discussed, respectively.
A hesitant fuzzy set hfs on is in terms of a function that when applied to returns a subset of, which can be represented as the following mathematical symbol. Pdf as uncertainty takes place almost everywhere in our daily life, many. As a generalization of fuzzy set, hesitant fuzzy set is a very useful tool in situations where there are some difficulties in determining the membership of an. In hesitant fuzzy decision making problems, the experts assign exact values for the membership of x in a hfs m.
Notes on distance and similarity measures of dual hesitant. Pdf picture hesitant fuzzy set and its application to. Hesitant fuzzy sets theory studies in fuzziness and soft computing. May 26, 2017 the hesitant fuzzy sets are a new efficient mathematical approach to study imprecise, uncertain, or incomplete knowledge. An entropy measure definition for finite intervalvalued. However, the classical soft sets are not appropriate to deal with.
Hesitant fuzzy soft set and its applications in multicriteria. Fuzzy multicriteria decision making algorithm under. Rodrguez, luis martnez, and francisco herrera, member, ieee abstractdealing with uncertainty is always a challenging 1 type2 fuzzy sets 6, 24 and typen fuzzy sets 6 that problem, and different tools have been proposed to deal with it. Zadeh, fuzzy sets, information and control 8 1965 338353. Similarity and entropy measures for hesitant fuzzy sets. On unification of methods in theories of fuzzy sets, hesitant. Abstract through this paper pentagonal hesitant fuzzy set. Pdf by using type2 fuzzy sets and hesitant fuzzy sets, type2 hesitant fuzzy sets are defined and their mathematical structure and characteristics. Torra, hesitant fuzzy sets, international journal of intelligent systems 25 2010 529539. For this purpose concepts of hesitant fuzzy relations are discussed first. Aug 10, 20 information measures for intervalvalued hesitant fuzzy sets.
The electre i mcdm method based on hesitant fuzzy sets 657 64. Hesitant fuzzy information aggregation in decision making. The aim of this manuscript is to apply hesitant fuzzy set for dealing with several kinds of theories in completely regular semigroups. Information measures for hesitant fuzzy sets and interval.
Introduction the hesitant fuzzy problems are common in daily life, which have been initially interpreted by torra1 as. According to the proposed method, the computational procedures of the problem are summarized as follows. Xu and xia 2011 developed the distance and similarity measures for hfss and proposed an approach based on distance measures for madm problems. A type2 fuzzy set enables us to define the membership of a given element in terms of a fuzzy set. Given a reference set x, a fuzzy set fs aon x is in terms of the function x 0,1. Although from a formal point of view, they can be seen as fuzzy multisets, we will show that their interpretation differs from the two existing approaches for fuzzy. Generalized hesitant fuzzy sets and their application in. It is proven that ad hoc defined basic concepts in individual theories, such as concepts of power set structures in these theories, relations or. One of the recent extensions to fuzzy sets is the introduction of hesitant fuzzy sets by torra 2010, torra and narukawa 2009. Introduction a number of realworld problems are extremely complex, since they involve. Rule based fuzzy systemshesitant fuzzy sets theoryconcepts and fuzzy. Pythagorean hesitant fuzzy sets are widely watched because of their excellent ability to deal with uncertainty, imprecise and vague information.
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